论文标题
统计模型和Fisher指标上的自然微分结构
Natural differentiable structures on statistical models and the Fisher metric
论文作者
论文摘要
在本文中，我讨论了费舍尔度量标准的概念与概率措施家族的可不同性概念之间的关系。我比较了平滑统计流形的概念，可区分的度量家族，$ k $积分的参数化度量模型，差异学统计模型，可区分的措施，这些措施在信息几何形状，数学统计和措施理论中产生，并讨论一些相关问题。
In this paper I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability measures. I compare the concepts of smooth statistical manifolds, differentiable families of measures, $k$-integrable parameterized measure models, diffeological statistical models, differentiable measures, which arise in Information Geometry, mathematical statistics and measure theory, and discuss some related problems.
